{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Data Analysis, 3rd ed\n",
    "##  Chapter 4, demo 1\n",
    "\n",
    "Normal approximaton for Bioassay model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import optimize, stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "# add utilities directory to path\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import psis\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)\n",
    "# apply custom background plotting style\n",
    "plt.style.use(plot_tools.custom_styles['gray_background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Bioassay data, (BDA3 page 86)\n",
    "x = np.array([-0.86, -0.30, -0.05, 0.73])\n",
    "n = np.array([5, 5, 5, 5])\n",
    "y = np.array([0, 1, 3, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compute the posterior density in grid\n",
    "#  - usually should be computed in logarithms!\n",
    "#  - with alternative prior, check that range and spacing of A and B\n",
    "#    are sensible\n",
    "ngrid = 100\n",
    "A = np.linspace(-4, 8, ngrid)\n",
    "B = np.linspace(-10, 40, ngrid)\n",
    "ilogit_abx = 1 / (np.exp(-(A[:,None] + B[:,None,None] * x)) + 1)\n",
    "p = np.prod(ilogit_abx**y * (1 - ilogit_abx)**(n - y), axis=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sample from the grid\n",
    "nsamp = 1000\n",
    "samp_indices = np.unravel_index(\n",
    "    np.random.choice(p.size, size=nsamp, p=p.ravel()/np.sum(p)),\n",
    "    p.shape\n",
    ")\n",
    "samp_A = A[samp_indices[1]]\n",
    "samp_B = B[samp_indices[0]]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "samp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "samp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50\n",
    "samp_ld50 = -samp_A / samp_B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the mode by minimising negative log posterior. Compute gradients and Hessian analytically, and use Newton's method for optimisation. You may use optimisation routines below for checking your results. See help for scipy.optimize.minimize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define the optimised function\n",
    "def bioassayfun(w):\n",
    "    a = w[0]\n",
    "    b = w[1]\n",
    "    et = np.exp(a + b * x)\n",
    "    z = et / (1 + et)\n",
    "    e = - np.sum(y * np.log(z) + (n - y) * np.log(1 - z))\n",
    "    return e\n",
    "# initial guess\n",
    "w0 = np.array([0.0, 0.0])\n",
    "# optimise\n",
    "optim_res = optimize.minimize(bioassayfun, w0)\n",
    "# extract desired results\n",
    "w = optim_res['x']\n",
    "S = optim_res['hess_inv']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the normal approximation density in grid. Note tha this is just for the illustration and in real case we would not need to evaluate this, and we would only use the draws from the normal distribution approaximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Construct a grid array of shape (ngrid, ngrid, 2) from A and B. Although\n",
    "# Numpy's concatenation functions do not support broadcasting, a clever trick\n",
    "# can be applied to overcome this without unnecessary memory copies\n",
    "# (see Numpy's documentation for strides for more information):\n",
    "A_broadcasted = np.lib.stride_tricks.as_strided(\n",
    "    A, shape=(ngrid,ngrid), strides=(0, A.strides[0]))\n",
    "B_broadcasted = np.lib.stride_tricks.as_strided(\n",
    "    B, shape=(ngrid,ngrid), strides=(B.strides[0], 0))\n",
    "grid = np.dstack((A_broadcasted, B_broadcasted))\n",
    "p_norm = stats.multivariate_normal.pdf(x=grid, mean=w, cov=S)\n",
    "\n",
    "# draw samples from the distribution\n",
    "samp_norm = stats.multivariate_normal.rvs(mean=w, cov=S, size=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute Pareto smoothed importance sampling weights and Pareto diagnostic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pareto khat is 0.79\n"
     ]
    }
   ],
   "source": [
    "lg = stats.multivariate_normal.logpdf(x=samp_norm, mean=w, cov=S)\n",
    "Ar = samp_norm[:,0]\n",
    "Br = samp_norm[:,1]\n",
    "ilogit_abx = 1 / (np.exp(-(Ar[:,None] + Br[:,None] * x)) + 1)\n",
    "lp = np.sum(np.log(ilogit_abx**y * (1 - ilogit_abx)**(n - y)), axis=1)\n",
    "lw = lp - lg\n",
    "lw, pk = psis.psislw(lw)\n",
    "print(\"Pareto khat is {:.2}\".format(pk))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importance sampling weights could be used to weight different expectations directly, but for visualisation and easy computation of LD50 histogram, we use resampling importance sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# resampling importance sampling\n",
    "pis = np.exp(lw)\n",
    "nsamp = 1000\n",
    "samp_indices = np.random.choice(pis.size, size=nsamp, p=pis)\n",
    "rissamp_A = Ar[samp_indices]\n",
    "rissamp_B = Br[samp_indices]\n",
    "# add random jitter, see BDA3 p. 76\n",
    "rissamp_A += (np.random.rand(nsamp) - 0.5) * (A[1]-A[0])\n",
    "rissamp_B += (np.random.rand(nsamp) - 0.5) * (B[1]-B[0])\n",
    "\n",
    "# samples of LD50\n",
    "rissamp_ld50 = - rissamp_A / rissamp_B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create figure with all results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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4Vldgqc2xgjEGAIYeEU4AAAAAQFcQ4RxUcXuNjChmZusT7059fWEgP8IZ3rWvKwzkRzjH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Nb8wdgbmG/8/j2H0YKg9W8bV9VyNprgy5ZJwKI5QZ66YxEKcIslqVPQd4rauqMsmh3gaF+MtAbx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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd47cb48160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 3, figsize=(13, 10))\n",
    "\n",
    "# plot the posterior density\n",
    "ax = axes[0, 0]\n",
    "ax.imshow(\n",
    "    p,\n",
    "    origin='lower',\n",
    "    aspect='auto',\n",
    "    extent=(A[0], A[-1], B[0], B[-1])\n",
    ")\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.grid('off')\n",
    "\n",
    "# plot the samples\n",
    "ax = axes[1, 0]\n",
    "ax.scatter(samp_A, samp_B, 5)\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.text(0, -7, 'p(beta>0)={:.2f}'.format(np.mean(samp_B>0)))\n",
    "\n",
    "# plot the histogram of LD50\n",
    "ax = axes[2, 0]\n",
    "ax.hist(samp_ld50, np.linspace(-0.8, 0.8, 31))\n",
    "ax.set_xlim([-0.8, 0.8])\n",
    "ax.set_xlabel(r'LD50 = -$\\alpha/\\beta$')\n",
    "ax.set_yticks(())\n",
    "ax.set_xticks(np.linspace(-0.8, 0.8, 5))\n",
    "\n",
    "# plot the posterior density for normal approx.\n",
    "ax = axes[0, 1]\n",
    "ax.imshow(\n",
    "    p_norm,\n",
    "    origin='lower',\n",
    "    aspect='auto',\n",
    "    extent=(A[0], A[-1], B[0], B[-1])\n",
    ")\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "ax.grid('off')\n",
    "\n",
    "# plot the samples from the normal approx.\n",
    "ax = axes[1, 1]\n",
    "ax.scatter(samp_norm[:,0], samp_norm[:,1], 5)\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "\n",
    "# Normal approximation does not take into account that the posterior\n",
    "# is not symmetric and that there is very low density for negative\n",
    "# beta values. Based on the samples from the normal approximation\n",
    "# it is estimated that there is about 4% probability that beta is negative!\n",
    "ax.text(0, -7, 'p(beta>0)={:.2f}'.format(np.mean(samp_norm[:,1]>0)))\n",
    "\n",
    "# Plot the histogram of LD50\n",
    "ax = axes[2, 1]\n",
    "# Since we have strong prior belief that beta should not be negative we can\n",
    "# improve our normal approximation by conditioning on beta>0.\n",
    "bpi = samp_norm[:,1] > 0\n",
    "samp_ld50_norm = - samp_norm[bpi,0] / samp_norm[bpi,1]\n",
    "ax.hist(samp_ld50_norm, np.linspace(-0.8, 0.8, 31))\n",
    "ax.set_xlim([-0.8, 0.8])\n",
    "ax.set_xlabel(r'LD50 = -$\\alpha/\\beta$')\n",
    "ax.set_yticks(())\n",
    "ax.set_xticks(np.linspace(-0.8, 0.8, 5))\n",
    "\n",
    "# plot the samples from the resampling importance sampling\n",
    "ax = axes[1, 2]\n",
    "ax.scatter(rissamp_A, rissamp_B, 5)\n",
    "ax.set_xlim([-2, 6])\n",
    "ax.set_ylim([-10, 30])\n",
    "ax.set_xlabel(r'$\\alpha$')\n",
    "ax.set_ylabel(r'$\\beta$')\n",
    "\n",
    "# Importance sampling is able to improve the estimate of p(beta>0)\n",
    "ax.text(0, -7, 'p(beta>0)={:.2f}'.format(np.mean(rissamp_B>0)))\n",
    "\n",
    "# Plot the histogram of LD50\n",
    "ax = axes[2, 2]\n",
    "ax.hist(rissamp_ld50, np.linspace(-0.8, 0.8, 31))\n",
    "ax.set_xlim([-0.8, 0.8])\n",
    "ax.set_xlabel(r'LD50 = -$\\alpha/\\beta$')\n",
    "ax.set_yticks(())\n",
    "ax.set_xticks(np.linspace(-0.8, 0.8, 5))\n",
    "\n",
    "# hide unused subplot\n",
    "axes[0, 2].axis('off')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that normal approximation centered at the posterior mode is able to catch some of the posterior shape, but the gives much larger value for $p(\\beta>0)$ and longer tails for the marginal posterior of LD50. The importance sampling is able to partially correct the normal approaximation, although it's clearly missing part of the mass in long tail of the true distribution, but still we get much improved approximation for the marginal posterior of LD50."
   ]
  }
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